Let M be a simple algebra A-module. (a) D = Hom A (M,M) is a division algebra
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Let M be a simple algebra A-module.
(a) D = HomA(M,M) is a division algebra over K, where HomA(M,M) denotes all endomorphisms of the algebra A-module M.
(b) M is a left algebra D-module.
(c) The ring HomD(M,M) of all D-algebra endomorphisms of M is a K-algebra.
(d) The map A - HomD(M,M) given by r|→ ar (where ar(x) = rx) is a K-algebra homomorphism.
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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